摘要
An approach to identifying fuzzy models considering both interpretability and precision was proposed. Firstly, interpretability issues about fuzzy models were analyzed. Then, a heuristic strategy was used to select input variables by increasing the number of input variables, and the Gustafson-Kessel fuzzy clustering algorithm, combined with the least square method, was used to identify the fuzzy model. Subsequently, an interpretability measure was described by the product of the number of input variables and the number of rules, while precision was weighted by root mean square error, and the selection objective function concerning interpretability and precision was defined. Given the maximum and minimum number of input variables and rules, a set of fuzzy models was constructed. Finally, the optimal fuzzy model was selected by the objective function, and was optimized by a genetic algorithm to achieve a good tradeoff between interpretability and precision. The performance of the proposed method was illustrated by the well-known Box-Jenkins gas furnace benchmark; the results demonstrate its validity.
提出一种同时考虑解释性和精确性的模糊建模方法.首先分析影响模糊模型解释性的主要因素,然后利用启发式搜索策略实现输入变量选择,利用模糊聚类算法和最小二乘辨识模糊模型.随后以输入变量数目和模糊规则数目的乘积衡量可解释性,以均方误差衡量精确性,并据此定义模型选择目标函数.最后给定最大最小的输入变量数目和规则数目,辨识得到一组模糊模型,利用模型选择目标函数,选择最优的模糊模型,并采用遗传算法进行优化,达到解释性与精确性的折衷.煤气炉仿真例子验证了该方法的有效性.
基金
TheNationalNaturalScienceFoundationofChina(No.60174019).
